OFFSET
0,2
COMMENTS
A transform of A000302 under the mapping g(x) ->(1/(1+x^3)) * g(x/(1+x^3)).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,0,-1).
FORMULA
a(n) = 4*a(n-1) - a(n-3).
a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k, k)*(-1)^k*4^(n-3*k).
MATHEMATICA
CoefficientList[Series[1/(1-4x+x^3), {x, 0, 30}], x] (* Harvey P. Dale, Apr 01 2011 *)
LinearRecurrence[{4, 0, -1}, {1, 4, 16}, 30] (* G. C. Greubel, Aug 03 2023 *)
PROG
(Magma) [n le 3 select 4^(n-1) else 4*Self(n-1) -Self(n-3): n in [1..30]]; // G. C. Greubel, Aug 03 2023
(SageMath)
@CachedFunction
def a(n): # a = A099503
if (n<3): return 4^n
else: return 4*a(n-1) - a(n-3)
[a(n) for n in range(31)] # G. C. Greubel, Aug 03 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 20 2004
STATUS
approved